Highly efficient ultra-broad beam silicon nanophotonic antenna based on near-field phase engineering

Optical antennas are a fundamental element in optical phased arrays (OPA) and free-space optical interconnects. An outstanding challenge in optical antenna design lies in achieving high radiation efficiency, ultra-compact footprint and broad radiation angle simultaneously, as required for dense 2D OPAs with a broad steering range. Here, we demonstrate a fundamentally new concept of a nanophotonic antenna based on near-field phase-engineering. By introducing a specific near-field phase factor in the Fraunhofer transformation, the far-field beam is widened beyond the diffraction limit for a given aperture size. We use transversally interleaved subwavelength grating nanostructures to control the near-field phase. A Bragg reflector is used at the end of the grating to increase both the efficiency and the far-field beam width. The antenna has a compact footprint of 3.1 µm × 1.75 µm and an ultra-broad far-field beam width of 52° and 62° in the longitudinal and transversal direction, respectively, while the radiation efficiency reaches 82% after incorporating a bottom reflector to further improve the directionality. This unprecedented design performance is achieved with a single-etch grating nanostructure in a 300-nm SOI platform.


Antenna far-field broadening
The far-field distribution generated by an optical antenna is related to the near field by the Fraunhofer transformation 32 : where E(x',y') is the complex amplitude at the aperture A located at x'y' plane, and k is the wave vector. For the Fraunhofer approximation to be valid, it is required that D 2 /Zλ < < 1, where D is the aperture width, Z is the distance between the aperture and the observation point, and λ is the wavelength 33 . This condition is always met by the operating far field conditions of practical OPAs. As described by Eq. (1), the shape and size of the antenna aperture directly affects the far-field distribution. While large beam widths in the far-field can be obtained by using small apertures, reducing the aperture size limits the antenna's efficiency.
Here, we propose a new strategy to circumvent this fundamental limit leveraging near-field phase engineering 34,35 . Instead of adjusting the antenna aperture, the key idea is to broaden the far-field by judiciously controlling the phase of the complex near-field E(x',y'). By introducing a specific near-field phase factor in the Fraunhofer transformation, the far-field beam width can be widened without shortening the antenna. This strategy allows us to decouple the minimum antenna length (required to ensure a given scattering efficiency) from the far-field beam width.
The near-field phase could be altered by longitudinally chirping the antenna grating period. However, as we show later in the longitudinally-chirped antenna section, for short antennas with strong radiation strength the chirping effect is ineffective because the antenna comprises only a small number of periods (e.g., [3][4][5] and their respective contributions to the scattered field are rapidly decreasing along the antenna. If a conventional longitudinal chirp is implemented in such short antennas, the contribution of the last periods to the scattered field is substantially smaller compared to the first period. This constraint fundamentally limits the effectiveness of chirping. Instead of chirping the grating longitudinally, here we use, for the first time, transversally-interleaved chirped nanostructures to control the near-field phase. With transverse chirping, the different chirp periods equally contribute to the scattered field, enabling effective phase engineering in very short gratings (few period) and yielding a substantially broadened far-field radiation compared to the conventional antennas.

Design and simulation results
Periodic grating antenna. As a reference case of an antenna with high scattering efficiency 36 , we consider a single-etch, periodic grating in a standard SOI platform with a 300-nm-thick silicon waveguide core, 1-μm buried oxide (BOX) and 2-μm oxide cladding. The grating comprises three periods, each including two fully etched sections with lengths L 1 and L 3 and two un-etched sections with length L 2 and L 4 , as schematically shown in Fig. 1.
The four geometrical parameters L 1 -L 4 are optimized using a genetic algorithm combined with 2D Finite-Difference Time-Domain (FDTD) simulations in order to achieve the maximum upward diffraction efficiency while the diffraction angle is allowed to vary as a free parameter. The detailed optimization procedure can be found in our previous work 31 . The optimized parameters are L 1 = 109 nm, L 2 = 48 nm, L 3 = 189 nm, L 4 = 387 nm, www.nature.com/scientificreports/ and Λ g = 733 nm, while the full antenna length is 2.2 μm. Rigorous 3D FDTD simulations are then used to validate the results of the 2D design. The antenna width for this structure is chosen as 1.75 μm, to yield a compact design required for dense antenna arrays. The upward diffraction efficiency at λ = 1550 nm obtained from 2D and 3D simulations is 60% and 55%, respectively, while the grating reflectivity (computed as the fraction of back-reflected power coupled to the counter propagating TE mode of the input waveguide) is − 20 dB (2D) and − 12 dB (3D). It should be noted that shortening the grating further and using two grating periods instead of three would significantly reduce the diffraction efficiency by 11%, while adding a fourth period would only increase efficiency by 2%. Figure 2 shows the far-field radiation pattern for the reference antenna design, where θ and ϕ represent the polar and azimuthal angles, respectively. The peak diffraction angle is 7° from the vertical, and the full width at half maximum (FWHM) of the far-field intensity along the longitudinal (x) and transverse (y) directions is 36° and 50° at 1550 nm, respectively.
Longitudinally-chirped antenna. In order to evaluate the effect of longitudinal chirping on the far-field beam width, we design an antenna with the structure described in periodic grating antenna section, but considering different periods for the three unit cells. The goal is to engineer the near-field phase profile of the diffracted beam in order to increase the divergence and obtain a broader beam width in the far-field. Simulating a range of grating periods showed that Λ g1 < 600 nm results in significant reduction in upward diffraction efficiency. The first cell period was hence designed to provide a large negative diffraction angle of -21°. Cell parameters were optimized as described in the previous section, resulting in L 1 = 133 nm, L 2 = 61 nm, L 3 = 190 nm, and L 4 = 216 nm (period Λ g1 = 600 nm). For the second cell, we use the optimized structural parameters from the reference design of periodic grating antenna section (Λ g2 = 733 nm, diffraction angle of 7°). For the last cell period we choose a positive diffraction angle of 9°, which still avoids second-order diffraction. The optimized parameters are L 1 = 109 nm, L 2 = 41 nm, L 3 = 300 nm, and L 4 = 350 nm, i.e., a cell period of Λ g3 = 800 nm. The width of the antenna is 1.75 μm, the same as the reference structure. 3D FDTD was used to simulate the behavior of the longitudinally-chirped grating. We obtained a FWHM of the far-field beam of 38° and 50.2° in the x and y directions, respectively. Diffraction efficiency was reduced to 45% compared to reference design, while maintaining comparable back-reflection (-10 dB). Despite the large chirping from Λ g1 = 600 nm to Λ g3 = 800 nm, the beam width in the longitudinal direction increased only marginally by 2°, indicating the limited effectiveness of longitudinal chirping to broaden the far-field of short antennas.
Transversally-interleaved chirped antenna. As described in antenna far-field broadening section, we propose to overcome the ineffectiveness of longitudinal chirping in few-period antennas using transversal chirping.
Instead of chirping the grating period along the propagation direction, the antenna is implemented by transversally interleaving two gratings with different longitudinal periods, as schematically shown in Fig. 3. Unlike traditional chirped grating, transverse chirping allows for the different chirp periods to equally contribute to the scattered field because the scatterers are arranged in parallel rather than sequentially. We used two of the optimized grating designs described in the longitudinally-chirped antenna section, the first with diffraction angle of − 21° (longitudinal period 600 nm) and the second with diffraction angle of 7° (longitudinal period 733 nm). The two gratings are transversally interleaved fourteen times with a subwavelength pitch of 125 nm, resulting in a total antenna width of 1.75 μm. Each grating has four periods along the longitudinal direction. We find that transversal chirping increases the far-field beam width in the longitudinal direction (as estimated At the end of the grating, there is part of the light that is left un-diffracted. Adding a Bragg reflector at the end of the grating will further improve grating efficiency by re-circulating the remaining power into the antenna. The reflector comprises two periods of silicon segment with a width of 148 nm separated by 152 nm gaps. The calculated Bragg mirror reflectivity is 95% at a wavelength of 1550 nm. The distance from the reflector to the antenna is judiciously optimized to obtain constructive interference between the forward propagating mode diffracted by the grating and the backward propagating mode diffracted upon reflection. The maximum upward diffraction efficiency of 51% is obtained for a reflector-grating separation of 300 nm, while only 5% of the power remains un-diffracted after the first pass through the antenna and the Bragg mirror. The calculated efficiency is comparable with that of the reference periodic grating, showing that we almost fully compensate the weakening of the grating strengths due to the chirping effect. Furthermore, the use of the Bragg reflector allows to further widen the far-field beam width in the longitudinal direction, as the result of the reversal of the diffraction angle. A gain of an additional 8° is observed in longitudinal beam width, yielding a wide far-field beam of 51° × 47° centered near −12°. In total, the beam width in the longitudinal direction is about 15° larger than the reference case while in transversal direction remains approximately unchanged. It is important to note that the increased beam divergence is obtained despite the aperture of the interleaved antenna (3 μm × 1.75 μm) being larger than that of the reference design (2.2 μm × 1.75 μm). This confirms that it is possible to circumvent the limitations on far-field beam size for a given antenna aperture by effectively engineering the near-field phase profile of the diffracted light.
Since a relatively large fraction of light (~ 30%) is diffracted downward, this light can be re-directed upward to further enhance the efficiency of the antenna. This is achieved by using a bottom reflector based on a double-SOI substrate, similar to that presented in 37 . The bottom Bragg reflector is designed by optimizing the thickness of the different layers in the double SOI structure. With a silicon thickness of 110 nm sandwiched between two silicon dioxide layers with thicknesses of 500 nm and 274 nm, a reflectivity of about 71% is obtained at the central wavelength of 1550 nm. By incorporating the bottom mirror in our antenna, a diffraction efficiency of 82% is obtained, the downward diffracted power is reduced to 8%, and the back-reflectivity of the antenna is -16 dB.
A detailed analysis of the behavior of the designed antenna is reported in Figs. 4 and 5. Figure 4 shows the amplitude of the electric field along the x-z cross-section taken at the center of the antenna. Power is primarily diffracted upward with a peak diffraction angle of -13°. Moreover, there is almost no power remaining in the waveguide after the Bragg reflector. Figure 5 illustrates the phase profiles of the scattered electric field for both    Fig. 4 and on a x-y plane placed 0.7 μm above the antenna. The curved phase front induced by the transversally-interleaved chirping can be clearly observed. Figure 6 shows the simulated far-field of the designed antenna. As can be seen, the additional phase curvature in the near-field obtained through transversal chirping translates into a wide far-field beam width of 52° × 62°. The peak diffraction angle is at -13° as expected from the near-field analysis.
Lastly, we performed a tolerance analysis to investigate the sensitivity of the optimized antenna design to fabrication imperfections. In particular, we evaluated the change in diffraction efficiency for segment length variations. The antenna shows a robust performance, i.e. less than a 6% reduction in diffraction efficiency, for fabrication bias of ± 5 nm, which is achievable using state-of-the-art silicon photonics manufacturing 38 .

Discussion and conclusion
In this paper, we demonstrate a new strategy based on near-field phase engineering to circumvent fundamental limitations on the beam width that can be achieved in optical antennas. Phase engineering is realized using transversally-interleaved subwavelength grating nanostructures followed by a Bragg reflector. Our optimized antenna design achieves a FWHM of 52° × 62°, a high diffraction efficiency of 82% (exploiting a bottom reflector), and an ultra-compact footprint of 3.15 μm × 1.75 μm. To compare our antenna with the state-of-the-art designs, we note that in ref. 39 a dual-input antenna based on two waveguides placed on opposite sides of a surface grating was used to increase the beam width. While this approach implements a concept similar to the use of a Bragg reflector that we propose here, it adds the additional burden of having two inputs with a perfectly controlled phases to properly work. Moreover, the angular range of the aforementioned design is limited to 40° × 15° for an effective antenna aperture of 2.5 μm 2 , much smaller compared to our design result reported here. This confirms once more the effectiveness of our transverse chirping strategy in substantially broadening the antenna far-field. We expect that exploration of near-field phase engineered nanostructures and integrated photonic components using transverse interleaved subwavelength gratings will lead to a new research direction in the development of integrated photonics antennas for a wide range of applications, including free-space optical interconnects and on-chip optical phased arrays for lidar systems.

Data availability
Data generated or analyzed in this study may be obtained from the contact author upon reasonable request.